The value of $lim x \to 0 ([\frac{100 x}{s i n x}] + [\frac{99 s i n x}{x}])$ ,where [.] denotes the greatest integer function, is

197

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198

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199

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Solution

The correct option is B
198

For x > 0, sin x < x

$\Rightarrow \frac{s i n x}{x} < 1$

$∴ \frac{99 s i n x}{x} < 99$

$\Rightarrow [\frac{99 s i n x}{x}]$ = 98

and $\frac{x}{s i n x} > 1$

$∴ \frac{100 x}{s i n x} > 100$

$\Rightarrow [\frac{100 x}{s i n x}]$ = 100

$∴ lim x \to 0 ([\frac{100 x}{s i n x}] + [\frac{99 s i n x}{x}])$ = 100+98 = 198

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The value of $lim x \to a ([\frac{100 x}{s i n x}] + [\frac{99 s i n x}{x}])$ ,where [.] denotes the greatest integer function, is

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